Of course it exists, but instead of asking here, where it is full of random people and trolls, it would be better to look for information on your own. Reddit is full of morons but their subreddits on technology, computers and budgeting often give surprisingly good advice.
I bought a crappy laptop from like 2012 virtually for free recently, 2GB of ram and a crappy processor and it works just fine with the games you mention as well as programs I used for studying at the time. That said, it was practically unusable with Windows, but I never had a problem using Linux. The only problem can sometimes be browsing the Internet, but there are so many alternatives for heavy sites that it's honestly easy to ignore (e.g. YouTube's lightweight front ends). Steam is a bit slow since their last update where they added the new horrific UI but it's still usable.
My point is, if I got that kind of garbage cheap, I'm sure you can get something much better for that budget.